The Collaborative International Dictionary of English v.0.48:

Arcane \Ar*cane"\, a. [L. arcanus.]
   Hidden; secret. [Obs.] "The arcane part of divine wisdom."
   --Berkeley.
   [1913 Webster]

WordNet (r) 3.0 (2006):

arcane
    adj 1: requiring secret or mysterious knowledge; "the arcane
           science of dowsing"

Moby Thesaurus II by Grady Ward, 1.0:

79 Moby Thesaurus words for "arcane":
   abstract, abstruse, cabalistic, censored, classified, close,
   closed, concealed, cryptic, dark, deep, eerie, enigmatic, esoteric,
   extramundane, extraterrestrial, fey, hermetic, hidden, hush-hush,
   hypernormal, hyperphysical, impenetrable, inscrutable, latent,
   mysterious, mystic, mystical, numinous, occult, otherworldly,
   preterhuman, preternatural, preternormal, pretersensual, profound,
   psychic, recondite, restricted, secret, smothered, spiritual,
   stifled, superhuman, supernatural, supernormal, superphysical,
   supersensible, supersensual, suppressed, supramundane,
   supranatural, top secret, transcendental, transmundane, ulterior,
   unaccountable, unbreatheable, uncanny, under security, under wraps,
   undisclosable, undisclosed, undivulgable, undivulged, unearthly,
   unguessed, unhuman, unknowable, unrevealable, unrevealed, unspoken,
   untellable, untold, unutterable, unuttered, unwhisperable,
   unworldly, weird